Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FERMAT'S EQUATION OVER 2-BY-2 MATRICES

  • Chien, Mao-Ting (Department of Mathematics Soochow University) ;
  • Meng, Jie (Finance.Fishery.Manufacture Industrial Mathematics Center on Big Data Pusan National University)
  • Received : 2020.05.04
  • Accepted : 2020.12.09
  • Published : 2021.05.31
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Abstract

We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.

Keywords

Acknowledgement

Jie Meng was partially supported by National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (NRF-2017R1A5A1015722).

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